454 research outputs found
Mirror symmetry and quantization of abelian varieties
The paper consists of two sections. The first section provides a new
definition of mirror symmetry of abelian varieties making sense also over
-adic fields. The second section introduces and studies quantized
theta-functions with two-sided multipliers, which are functions on
non-commutative tori. This is an extension of an earlier work by the author. In
the Introduction and in the Appendix the constructions of this paper are put
into a wider context.Comment: 24 pp., amstex file, no figure
Спонтанний розрив стравоходу: нестандартна ситуація в діагностиці та лікуванні
Перфорації стравоходу належать до смертельно небезпечних захворювань. Серед усіх можливих варіантів даної патології окреме місце за тяжкістю діагностування та надання допомоги займає спонтанний розрив
Mirror duality and noncommutative tori
In this paper, we study a mirror duality on a generalized complex torus and a
noncommutative complex torus. First, we derive a symplectic version of Riemann
condition using mirror duality on ordinary complex tori. Based on this we will
find a mirror correspondence on generalized complex tori and generalize the
mirror duality on complex tori to the case of noncommutative complex tori.Comment: 22pages, no figure
Period- and mirror-maps for the quartic K3
We study in detail mirror symmetry for the quartic K3 surface in P3 and the
mirror family obtained by the orbifold construction. As explained by Aspinwall
and Morrison, mirror symmetry for K3 surfaces can be entirely described in
terms of Hodge structures. (1) We give an explicit computation of the Hodge
structures and period maps for these families of K3 surfaces. (2) We identify a
mirror map, i.e. an isomorphism between the complex and symplectic deformation
parameters, and explicit isomorphisms between the Hodge structures at these
points. (3) We show compatibility of our mirror map with the one defined by
Morrison near the point of maximal unipotent monodromy. Our results rely on
earlier work by Narumiyah-Shiga, Dolgachev and Nagura-Sugiyama.Comment: 29 pages, 3 figure
Mixed-symmetry massive fields in AdS(5)
Free mixed-symmetry arbitrary spin massive bosonic and fermionic fields
propagating in AdS(5) are investigated. Using the light-cone formulation of
relativistic dynamics we study bosonic and fermionic fields on an equal
footing. Light-cone gauge actions for such fields are constructed. Various
limits of the actions are discussed.Comment: v3: 24 pages, LaTeX-2e; typos corrected, footnote 7 and 2 references
added, published in Class. Quantum Gra
The Pure Virtual Braid Group Is Quadratic
If an augmented algebra K over Q is filtered by powers of its augmentation
ideal I, the associated graded algebra grK need not in general be quadratic:
although it is generated in degree 1, its relations may not be generated by
homogeneous relations of degree 2. In this paper we give a sufficient criterion
(called the PVH Criterion) for grK to be quadratic. When K is the group algebra
of a group G, quadraticity is known to be equivalent to the existence of a (not
necessarily homomorphic) universal finite type invariant for G. Thus the PVH
Criterion also implies the existence of such a universal finite type invariant
for the group G. We apply the PVH Criterion to the group algebra of the pure
virtual braid group (also known as the quasi-triangular group), and show that
the corresponding associated graded algebra is quadratic, and hence that these
groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies
corrected, reflecting suggestions made by the referee of the published
version of the pape
Supersymmetric Deformations of Maximally Supersymmetric Gauge Theories
We study supersymmetric and super Poincar\'e invariant deformations of
ten-dimensional super Yang-Mills theory and of its dimensional reductions. We
describe all infinitesimal super Poincar\'e invariant deformations of equations
of motion of ten-dimensional super Yang-Mills theory and its reduction to a
point; we discuss the extension of them to formal deformations. Our methods are
based on homological algebra, in particular, on the theory of L-infinity and
A-infinity algebras. The exposition of this theory as well as of some basic
facts about Lie algebra homology and Hochschild homology is given in
appendices.Comment: New results added. 111 page
Classical R-Matrices and the Feigin-Odesskii Algebra via Hamiltonian and Poisson Reductions
We present a formula for a classical -matrix of an integrable system
obtained by Hamiltonian reduction of some free field theories using pure gauge
symmetries. The framework of the reduction is restricted only by the assumption
that the respective gauge transformations are Lie group ones. Our formula is in
terms of Dirac brackets, and some new observations on these brackets are made.
We apply our method to derive a classical -matrix for the elliptic
Calogero-Moser system with spin starting from the Higgs bundle over an elliptic
curve with marked points. In the paper we also derive a classical
Feigin-Odesskii algebra by a Poisson reduction of some modification of the
Higgs bundle over an elliptic curve. This allows us to include integrable
lattice models in a Hitchin type construction.Comment: 27 pages LaTe
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